Mathematical Study for Traffic Flow and Traffic Density in Kigali Roads
Authors: Kayijuka Idrissa
This work investigates a mathematical study for traffic flow and traffic density in Kigali city roads and the data collected from the national police of Rwanda in 2012. While working on this topic, some mathematical models were used in order to analyze and compare traffic variables. This work has been carried out on Kigali roads specifically at roundabouts from Kigali Business Center (KBC) to Prince House as our study sites. In this project, we used some mathematical tools to analyze the data collected and to understand the relationship between traffic variables. We applied the Poisson distribution method to analyze and to know the number of accidents occurred in this section of the road which is from KBC to Prince House. The results show that the accidents that occurred in 2012 were at very high rates due to the fact that this section has a very narrow single lane on each side which leads to high congestion of vehicles, and consequently, accidents occur very frequently. Using the data of speeds and densities collected from this section of road, we found that the increment of the density results in a decrement of the speed of the vehicle. At the point where the density is equal to the jam density the speed becomes zero. The approach is promising in capturing sudden changes on flow patterns and is open to be utilized in a series of intelligent management strategies and especially in noncurrent congestion effect detection and control.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1129195Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1327
 Henry Lieu, Traffic-Flow Theory, Public Roads. US Dept of Transportation, Jan-Feb (1999), (Vol. 62 No. 4).
 D.C. Gazis, Traffic Theory, (Springer Berlin, 2002).
 N. Bellomo. V. Coscia, M. Delta, Math. Mod. App. Sc. 12, 1801-1843 (2002).
 Adolf D. May. Fundamentals of Traffic Flow, Prentice-Hall. Inc. Englewood Cliff New Jersey 07632, Second edition, 1990.
 Chowdhury, D., Santen, L. Schreckenberg, A., Statistics physics of vehicular traffic and some related systems. Phs. Rep. 329, 199-329 (2000).
 Loukas, S. Kemp, C. D. (1986). The index of Dispersion Test for the Bivariate Poison Distribution. Biometric. 42 (4): 941-948.
 Helbing, D., Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067-1141 (2001).
 Bellomo, N., Delitala, M., Coscia, V.: On the mathematical theory of vehicular traffic flow. I-fluid dynamic and kinematic modeling. Math. Models Methods Appl. Sci. 12, 1801-1843 (2002).
 Klar,A., Wegener, R.: Traffic flow: models and numerics. In: Modeling and Computational Methods for Kinematic Eqautions, pp. 219-258. Birha ̈user,Boston (2004).
 Lighthill, M.J., Whitham, G.B.: On kinematics waves: II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 229, 317-345 (1955)
 Richards, P.I.: Shock waves on the highway. Oper. Res. 4, 42-51 (1956).
 Payne, H.J.: Models or freeway traffic and control. In: Bekey, G.A. (ed.) Mathematical Models of Public System. Simulation Councils Processings Series, Vol. 1, pp. 51-61 (1971).
 Jiang, R., Wu, Q.S., Zhu, Z.J.: A new continuum model for traffic flow and numerical tests. Transp. Res., Part B, Methodol. 36, 405-419 (2002).
 Wong, G.C.K., Wong, S.C.: A multi-class traffic flow model-an extension of LWR model with heterogeneous drivers. Transp. Res., Part A, Policy Pract. 36, 827-841 (2002).
 Gupta, A.K., Katiyar, V.K.: A new multi-class continuum model for traffic flow. Transportmetrica 3, 73-85 (2007).
 Bando, M. Hasebe, K., Nakayama, A., Shibata, A., Sugiyama, Y.: Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51,1035-1042 (1995).
 Helbing, D., Tilch, B.: Generalized force model of traffic flow. Phys. Rev. E 58, 133-138 (1998).
 Nagatani, T.: Stabilization and enhancement of traffic flow by next-nearest-neighbor interaction. Phys. Rev. E 60, 6395-6401 (1998)
 Jiang, R., Wu, W.S., Zhu, Z.J.,: Full velocity difference model for car-following theory. Phys. Rev. E 64, 017101 (2001).
 Ge, H.X., Dia, S.Q., Dong, L.Y., Xue, Y.: Stabilization effect of traffic flow in extended car-flowing model based on intelligent transportation system application. Phys. Rev. E 70, 066134 (2004).
 Cassidy, M.J. and R. L. Bertini. “Some Traffic Features at freeway Bottlenecks” Methodological 33. 1 25-42 (1999).